Linear widths of weighted Sobolev classes with conditions on the highest order and zero derivatives

TL;DR

This paper derives order estimates for the linear widths of weighted Sobolev classes defined by restrictions on derivatives and zero derivatives in weighted $L_p$ norms, advancing understanding of their approximation properties.

Contribution

It provides new order estimates for the linear widths of specific weighted Sobolev classes with conditions on derivatives and zero derivatives.

Findings

Order estimates for linear widths are obtained.

Results apply to classes defined by weighted norms of derivatives.

Advances the theory of approximation in weighted Sobolev spaces.

Abstract

In this paper order estimates for the linear widths of some function classes are obtained; these classes are defined by restrictions on the weighted $L_{p_1}$-norm of the r-th derivative and the weighted $L_{p_0}$-norm of zero derivative.